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GRE^® Quantitative Reasoning

The GRE Quantitative Reasoning course teaches arithmetic, number properties, algebra, geometry, data analysis, and quantitative comparison techniques, enabling learners to solve multi‑step problems with speed and accuracy for graduate‑school entrance exams.

Who Should Take This

It is ideal for undergraduate seniors, recent graduates, or working professionals who plan to apply to graduate programs and need a solid grasp of high‑school and early‑college mathematics. These learners benefit from focused, exam‑style practice that reinforces definitions, formulas, and reasoning strategies, helping them achieve competitive scores on the GRE quantitative section.

What's Included in AccelaStudy® AI

Adaptive Knowledge Graph

Practice Questions

Lesson Modules

Console Simulator Labs

Exam Tips & Strategy

20 Activity Formats

Course Outline

77 learning goals

1 Arithmetic and Number Properties

5 topics

Integers and Divisibility

Define and identify prime numbers, composite numbers, factors, multiples, and divisibility rules for integers including 2, 3, 4, 5, 6, 8, 9, and 10.
Apply prime factorization to determine the greatest common factor and least common multiple of integers, and solve problems involving remainders when products or sums are divided by a given divisor.
Analyze properties of odd and even integers, positive and negative integers, and zero to determine outcomes of arithmetic operations and comparisons in quantitative problems.

Fractions, Decimals, and Percents

State the rules for performing arithmetic operations with fractions including finding common denominators, and describe the methods for converting between fractions, decimals, and percents.
Apply conversions between fractions, decimals, and percents to solve problems requiring comparison or calculation across different numerical representations.
Calculate percent increase, percent decrease, and successive percent changes, including problems where the base changes between successive applications.
Analyze multi-step percent problems involving compound changes, markups, discounts, taxes, and interest to determine the final value or original amount.

Exponents, Roots, and Absolute Value

List the laws of exponents including product, quotient, power, zero, and negative exponent rules, define nth roots and absolute value, and describe absolute value as distance on the number line.
Apply exponent rules to simplify expressions with integer and rational exponents, solve absolute value equations and inequalities, and convert between radical and exponential notation.
Analyze comparison problems involving exponential expressions with different bases and exponents, determining which quantity is greater without full computation.

Ratios, Rates, and Proportions

Define ratio, proportion, and rate, and describe how to set up and solve proportional relationships between two quantities.
Solve word problems involving ratios, proportions, direct and inverse variation, speed-distance-time relationships, and unit conversions using dimensional analysis.
Analyze complex rate problems involving multiple constraints such as combined work rates, upstream-downstream motion, or average speed over multiple legs of a journey.

Sequences and Patterns

Identify arithmetic and geometric sequences from their defining properties and state the formulas for the nth term and sum of a finite number of terms.
Apply sequence formulas to calculate specific terms, find partial sums, determine the common difference or ratio, and analyze repeating patterns to find terms at large position numbers.

2 Algebra

6 topics

Algebraic Expressions and Operations

List the rules for adding, subtracting, multiplying, and dividing algebraic expressions, including distribution, combining like terms, and factoring common factors.
Apply factoring techniques including greatest common factor, difference of squares, and trinomial factoring to simplify algebraic expressions and solve equations.

Linear Equations and Inequalities

Solve single-variable linear equations and inequalities, including compound inequalities, representing solution sets on a number line or in interval notation.
Solve systems of two linear equations in two variables using substitution and elimination methods, interpreting the solution as a point of intersection.
Analyze systems of linear equations to determine whether the system has one solution, no solution, or infinitely many solutions based on the relationship between the equations.

Quadratic Equations

State the quadratic formula, the relationship between the discriminant and the number of real solutions, and the methods for solving quadratics by factoring and completing the square.
Solve quadratic equations by factoring, completing the square, or applying the quadratic formula, selecting the most efficient method for each problem type.
Analyze word problems that lead to quadratic equations, setting up the equation from the problem context and interpreting solutions in terms of the original scenario.

Functions

Define function, domain, and range, recognize function notation, and describe how to evaluate f(x) for given values of x including expressions.
Interpret graphs of functions to determine domain, range, intercepts, extrema, and intervals of increase and decrease, and evaluate composite functions of the form f(g(x)).

Coordinate Geometry

State the distance formula, midpoint formula, and slope formula for two points in the coordinate plane, and list the forms of linear equations.
Apply the slope-intercept and point-slope forms to write the equation of a line, determine whether two lines are parallel or perpendicular, and find points of intersection.
Analyze coordinate geometry problems involving regions defined by linear inequalities, determining which areas satisfy given constraints and graphing solution regions.

Word Problems and Algebraic Modeling

Translate verbal descriptions into algebraic equations or systems, and solve age problems, digit problems, consecutive integer problems, and mixture problems.
Evaluate whether a word problem's solution is reasonable by checking units, verifying against given constraints, and confirming that the answer addresses what was asked.

3 Geometry

6 topics

Lines and Angles

Define and identify types of angles (acute, right, obtuse, straight), complementary and supplementary pairs, vertical angles, and the angle relationships formed by parallel lines cut by a transversal.
Apply angle relationships including corresponding, alternate interior, and co-interior angles formed by parallel lines and a transversal to calculate unknown angle measures.

Triangles

State the properties of triangles including the angle sum property, the triangle inequality theorem, and the side-length ratios for 30-60-90 and 45-45-90 special right triangles.
Apply the Pythagorean theorem to calculate unknown side lengths in right triangles and to verify whether a triangle with given side lengths is a right triangle.
Calculate the area and perimeter of triangles using the base-height formula, and apply properties of similar triangles including proportional sides and equal angles to find unknown dimensions.
Analyze composite geometry problems involving triangles inscribed in or circumscribed around other figures, determining unknown measurements through combined application of triangle properties.

Circles

Define radius, diameter, chord, arc, central angle, inscribed angle, tangent, and secant, and state the formulas for circumference and area of a circle.
Calculate arc length and sector area as fractions of the full circle, and apply the inscribed angle theorem and tangent-radius perpendicularity to determine unknown angles and lengths.
Analyze problems involving circles combined with triangles or other polygons, such as inscribed or circumscribed figures, using multiple geometric properties simultaneously.

Quadrilaterals and Polygons

State the properties and area formulas for parallelograms, rectangles, squares, rhombuses, and trapezoids, and describe the interior and exterior angle sum formulas for polygons.
Calculate the area and perimeter of regular and irregular polygons by decomposing them into triangles and rectangles, and compute individual angle measures in regular polygons.

Three-Dimensional Figures

State the formulas for volume and surface area of rectangular solids, cubes, cylinders, and right circular cones, identifying the required dimensions for each formula.
Calculate the volume and surface area of standard three-dimensional figures and solve problems involving the relationship between a figure's dimensions and its volume or surface area.
Analyze how changing one dimension of a three-dimensional figure affects its volume and surface area, using proportional reasoning to determine the scaling relationship.

Coordinate Geometry in Geometric Contexts

Apply the distance and midpoint formulas to solve geometry problems in the coordinate plane, including finding side lengths, perimeters, and areas of figures with vertices given as coordinate pairs.
Analyze coordinate geometry problems requiring integration of algebraic equations of lines and circles with geometric properties to determine intersections, distances, and enclosed areas.

4 Data Analysis

5 topics

Descriptive Statistics

Define mean, median, mode, range, standard deviation, variance, quartiles, interquartile range, and percentiles, and describe when each measure is most appropriate for summarizing data.
Calculate the mean, median, and mode for data presented in lists, frequency tables, and grouped frequency distributions, including weighted mean calculations.
Analyze how adding, removing, or changing data values affects the mean, median, mode, range, and standard deviation, and compare spreads of data sets without exact computation.

Data Interpretation from Graphs and Tables

Identify the key components of bar charts, line graphs, pie charts, histograms, scatterplots, and boxplots, including axes, scales, labels, and legends.
Interpret data values, trends, and patterns from bar charts, line graphs, and pie charts, including reading approximate values and calculating differences between data points.
Interpret histograms, frequency distributions, and boxplots to determine distribution shape, identify skewness, estimate central tendency, compare quartiles, and detect potential outliers.
Interpret scatterplots to assess the direction, form, and strength of association between two variables and conceptually identify the line of best fit.
Analyze data presented in complex multi-part tables and graphs, performing multi-step calculations such as weighted averages, percent changes, or cross-category ratios.

Probability

Define probability as a ratio of favorable to total outcomes, state the complement rule, and describe the range of probability values from zero to one.
Calculate probabilities of simple, compound, and conditional events using the addition rule, multiplication rule, and independence criteria for determining event relationships.
Analyze probability problems involving geometric probability, multi-stage experiments, and probability distributions derived from frequency tables or described scenarios.

Counting Methods

State the fundamental counting principle, define permutations and combinations with their formulas nPr and nCr, and describe factorial notation.
Apply permutations and combinations to count arrangements or selections in problems involving seating, committees, teams, and subsets from larger groups.
Determine when to use permutations versus combinations by analyzing whether the order of selection matters in the given problem context.

Normal Distribution

Describe the properties of the normal distribution including its bell shape, symmetry about the mean, and the empirical rule stating that approximately 68, 95, and 99.7 percent of data fall within one, two, and three standard deviations.
Apply the empirical rule to estimate the percentage of data falling within specified standard deviation intervals of the mean in a normally distributed data set.
Analyze problems comparing values from different normal distributions by standardizing scores and interpreting relative position within each distribution.

5 Quantitative Comparison Questions

2 topics

Quantitative Comparison Format and Strategy

Recognize the structure of Quantitative Comparison questions with Quantity A, Quantity B, shared constraints, and the four answer choices: A greater, B greater, equal, or cannot be determined.
Apply algebraic simplification to both quantities simultaneously and use the strategy of testing boundary and extreme values to determine whether the relationship between quantities can change.
Evaluate when a Quantitative Comparison answer is 'cannot be determined' by demonstrating that different allowable variable values produce different comparison outcomes.

Quantitative Comparison by Content Area

Analyze Quantitative Comparison problems involving number properties, determining the relationship between quantities based on constraints about integers, primes, divisibility, or sign.
Analyze Quantitative Comparison problems involving algebraic expressions, using substitution and simplification to compare polynomial, rational, or exponential quantities.
Analyze Quantitative Comparison problems involving geometric figures, comparing areas, perimeters, angles, or lengths using given diagram constraints and geometric theorems.
Analyze Quantitative Comparison problems involving data and statistics, comparing means, medians, standard deviations, or probabilities from described or displayed data sets.

6 Problem Solving and Data Interpretation Question Types

3 topics

Problem Solving Strategies

Recognize the three Problem Solving question formats (select one answer, select one or more answers, numeric entry) and identify the specific response requirements of each format.
Apply estimation, approximation, and back-solving techniques to efficiently eliminate wrong answer choices and verify the reasonableness of computed results.
Determine the optimal problem-solving strategy (algebraic, arithmetic, geometric, back-solving, or picking numbers) based on the structure and constraints of the given problem.

Data Interpretation Sets

Interpret multi-source data presentations and calculate derived quantities such as percent of total, per-capita values, year-over-year changes, and cross-category ratios from combined tables and graphs.
Evaluate claims or conclusions about trends, proportions, or relationships stated about data in tables and graphs, determining whether the data supports the stated claim.

Test Strategy and Time Management

Apply time-allocation strategies for the Quantitative Reasoning section, prioritizing questions by type and difficulty to maximize total correct answers within the time limit.
Evaluate which problems to attempt first and which to flag for review based on an assessment of problem complexity and personal mathematical strengths.

Scope

Included Topics

GRE General Test Quantitative Reasoning section (revised shorter GRE format, effective September 2023): Arithmetic, Algebra, Geometry, and Data Analysis covering all math content areas specified in the ETS GRE quantitative reasoning measure.
Arithmetic: properties of integers (divisibility, factorization, prime numbers, remainders), arithmetic operations, exponents and roots, estimation, percent, ratio, rate, absolute value, the number line, decimal representation, and sequences of numbers.
Algebra: operations with exponents, factoring and simplifying algebraic expressions, relations, functions, equations, inequalities, solving linear and quadratic equations and inequalities, solving simultaneous equations and inequalities, setting up equations to solve word problems, coordinate geometry including graphs of functions, equations and inequalities, intercepts, and slopes of lines.
Geometry: parallel and perpendicular lines, circles, triangles (including isosceles, equilateral, and 30-60-90 and 45-45-90 special right triangles), quadrilaterals, other polygons, congruent and similar figures, three-dimensional figures, area, perimeter, volume, surface area, the Pythagorean theorem, and angle measurement in degrees.
Data Analysis: basic descriptive statistics (mean, median, mode, range, standard deviation, interquartile range, quartiles, percentiles), interpretation of data in tables, bar graphs, circle graphs, line graphs, histograms, scatterplots, frequency distributions, and boxplots; elementary probability, combinatorics (permutations and combinations, counting principles), distributions of data, and the normal distribution.
Quantitative Comparison questions: comparing two quantities (Quantity A and Quantity B) and selecting whether A is greater, B is greater, the quantities are equal, or the relationship cannot be determined from the information given.
Data Interpretation question sets: answering multiple questions based on data presented in tables and graphs, including multi-step calculations and combined data source problems.
Problem Solving questions: multiple-choice (select one or select one or more) and numeric entry questions requiring direct computation, estimation, or strategic reasoning.

Not Covered

GRE Verbal Reasoning section content including reading comprehension, text completion, sentence equivalence, and vocabulary.
GRE Analytical Writing section content including Issue and Argument essay tasks.
Advanced mathematics beyond the GRE scope: calculus, trigonometry (beyond basic right-triangle ratios), linear algebra, abstract algebra, real analysis, differential equations, and advanced probability theory.
GRE Subject Test mathematics content and proofs-based mathematics.
Calculator-specific strategies for the on-screen calculator beyond basic awareness of its availability; programming or coding-related math.
Test administration logistics, registration procedures, scoring algorithms, and section-level adaptive testing mechanics.